Turkish President Recep Tayyip Erdogan and his US counterpart, Donald Trump, have discussed the situation in northern Syria over the phone amid rising tensions over the fate of Kurdish fighters in the war-torn country.

The conversation on Monday came a day after Trump threatened on Twitter that he would "devastate" Turkey's economy if its forces attacked the US-backed Kurdish fighters, who helped Washington in its fight against the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group.

The war of words between the two NATO allies is the latest consequence of Trump's surprising decision last month to withdraw US troops from northern Syria, potentially leaving the Kurdish militia under threat as Ankara weighs a new offensive there.

In a statement, the Turkish presidency said Erdogan told Trump he had no problem with Kurds in Syria and that Ankara is only seeking to fight armed groups in the war-ravaged country which threaten its national security.

The two leaders also "discussed the idea of creating a security zone cleared of terrorism in the north of the country", the statement added.

Trump confirmed this in a tweet later, but referred to the proposed area as a "safe zone".

He did not gave any details about the safe zone proposal, but US Secretary of State Mike Pompeo said Washington wanted to provide security for those who have fought ISIL and to prevent any attack on Turkey from Syria.

Sarah Sanders, White House press secretary, said in a statement: "The president expressed the desire to work together to address Turkey's security concerns in northeast Syria while stressing the importance to the United States that Turkey does not mistreat the Kurds and other Syrian Democratic Forces with whom we have fought to defeat ISIS."

According to the White House, Joint Chiefs Chairman Joseph Dunford is set to meet with his Turkish counterpart, Yasar Guler, on Tuesday for further consultations.

'A highly unreliable partner'

Ankara considers the US-allied Kurdish People's Protection Units (YPG) and its political wing - the Kurdish Democratic Union Party (PYD) - to be "terrorist groups" with ties to the banned Kurdistan Workers' Party (PKK) in Turkey.

For weeks, it has vowed to carry out military operations against the YPG, and has condemned the US for its military relationship with the Kurdish fighters.

The Trump administration has defended its relationship with the YPG, and on Sunday the US president vowed to "devastate Turkey economically" if it targeted them.

Starting the long overdue pullout from Syria while hitting the little remaining ISIS territorial caliphate hard, and from many directions. Will attack again from existing nearby base if it reforms. Will devastate Turkey economically if they hit Kurds. Create 20 mile safe zone....

— Donald J. Trump (@realDonaldTrump) January 13, 2019

....Likewise, do not want the Kurds to provoke Turkey. Russia, Iran and Syria have been the biggest beneficiaries of the long term U.S. policy of destroying ISIS in Syria - natural enemies. We also benefit but it is now time to bring our troops back home. Stop the ENDLESS WARS!

— Donald J. Trump (@realDonaldTrump) January 13, 2019

In response, Turkey's Foreign Minister Mevlut Cavusoglu said "we are not scared of and will not be intimidated by any threats", adding that "economic threats against Turkey will get nowhere."

Turkey has said the US administration has been incoherent about the withdrawal process since Trump's December 19 announcement that he would pull some 2,000 US troops out of Syria, as well as in its approach to different "terrorist groups".

Yasin Aktay, an adviser to Erdogan, said the US has been "a highly unreliable partner" to Ankara.

"The problems and misunderstandings between the US and Turkey are results of the confusion and cacophony between the actors at different levels of the US administration and institutions," he told Al Jazeera.

Turkey's state-run Anadolu Agency reported that the two leaders also discussed the need to complete a roadmap regarding Syria's border town of Manbij, so as to avoid giving any opportunity to elements seeking to block the planned withdrawal of US forces.

Turkish and US troops began joint patrols in Manbij on November 1 as part of an agreement that focuses on the withdrawal of YPG fighters from the city to stabilise the region.

Last month, Trump's withdrawal announcement several politicians in Washington as well as Western and Kurdish allies fighting alongside the US.

Trump's decision was initially expected to be carried out swiftly, but the timetable became vague in the weeks following his announcement.

France, Britain and local armed groups have also warned that ISIL has not been totally defeated yet.